For someone's future reference - or if you are still considering the jump yourself, MDSW's ISO/IEC 62304 is Aerospace's DO-178C. The AS9100 and ARPA4754 of Aerospace is the 13485 of Medical Device (+ some specific FDA Guidance on Connected/Electronic Systems that are not directly captured by the ISO standards).
Whereas DAL seems to have a strong focus on availability of systems (reliability, redundancy etc.) in its assessment of Severity and classification of "System" levels, Medical Device Software is typically more focused on integrity (and more recently, confidentiality for Cloud-based systems) and obviously, foreseeable use and misuse of systems by its users. Essentially, only few Medical Devices have catastrophic outcomes in case of unavailability, but incorrect medicinal dosing algorithms are typically considered catastrophic. ISO 62304 operates with Class A-C Software Systems, a classification determined by the harm in case of a failure; a determination grounded in the intended use, clinical assessment and ISO 14971 Risk Assessment of the medical device.